Support Vector Machines and the curse of dimensionality I am reading this paper: "Automated MR image classification in temporal lobe epilepsy", by Focke et al. NeuroImage, 2012. 
The authors use support vector machines to classify subjects between healthy controls and patients with epilepsy using magnetic resonance images using leave-one-out cross validation. 
Every image provides features in the order of hundreds of thousands. However there are only 38 patients and 22 controls (observations).
In your opinion, is there any problem/disadvantage with this design?
In a situation like this, I would use feature selection and/or dimensionality reduction before classification. It seems intuitive to get rid of uninformative features first.
However, I understand that in the boundary optimization problem associated with SVMs, non informative dimensions are be assigned a low weight, even a zero coefficient. Then, is there then any argument for feature selection prior to SVM training other than facilitate convergence of the optimization problem? 
 A: Generally, when doing classification in $p\gg n$ conditions you have a non-negligible chance that some combination of irrelevant attributes will be well correlated with the decision by pure chance, thus yielding deceivingly good classification accuracy and hiding real associations, if any are actually in the data.   
Greedy, non-nested feature selection will likely make things worse because real correlations are usually weaker than best spurious ones, and thus will be distilled out; on the same time dimension reduction will further improve the reported accuracy, reaffirming the false impression that everything is OK (this is called overfitting by feature selection). 
In other words, doing feature selection has a fair amount of significant benefits (some insight in a problem, better accuracy, simpler training), but may be very dangerous -- thus, well, when there is not enough training samples to do a full-blown validation it is certainly better not to do feature selection than to do it wrong.
